An adopted article adapted here:
1) UPnP
UPnP, which stands for Universal Plug and Play, is a massively complex standard that does about a million different things. Among all these different capabilities lies the Internet Gateway Device protocol, which allows LimeWire to ask the router to open required ports for it. By default this is usually port 6346.
UPnP is supported by most home routers made in the last couple of years, with the notable exception of Apple's Airport Base Stations.
2) NAT-PMP
NAT-PMP happened when Apple looked at the giant mess that is UPnP and decided they'd rather make their own protocol. They were a little slow in getting it out, but as of July 2005 with Airport 4.2, Apple's Airport Extreme and Airport Express base stations now support it. It's completely unrelated to UPnP, but the end result is the same, and you, the user, should not see any difference.
Unfortunately, NAT-PMP is off by default. To enable it, first make sure you have Airport 4.2 or later (available in Software Update), then run the AirPort Admin Utility. If it asks you to update your base station's firmware, make sure that you do so, as NAT-PMP requires the latest firmware. Go to the "AirPort" tab and click the "Base Station Options..." button. In the sheet that drops down, turn on the "Enable NAT Port Mapping Protocol" checkbox in the "Ethernet Port Security" tab. Ignore the erroneous note Apple has placed regarding 10.4 - LimeWire will work with NAT-PMP on OS X 10.3 as well (see sample image below.) Click OK, then click Update and the router will restart. As with UPnP, you'll have to restart LimeWire for it to be able to see the change.
3) If you have problems with NAT-PMP or your OSX version doesn't support it, then you may need to manually forward the necessary port for LimeWire. See
Configuring AirPort Extreme for LimeWire